MODELING PHYSICAL SYSTEMS BY EFFECTIVE HARMONIC-OSCILLATORS - THE OPTIMIZED QUADRATIC APPROXIMATION

A mathematical formalism is developed to map a physical system described by a general potential energy function onto one consisting of effective harmonic oscillators. The present focus is on many-body systems characterized by a temperature, so the theoretical effort is devoted to the partition function through a diagrammatic representation of its cumulant expansion in the quadratic reference system. Appropriate diagram summation and renormalization strategies lead to an "optimized quadratic approximation" (OQA) for both the quantum and classical partition functions of general systems. Diagrammatic methods are also used to develop accurate higher order corrections to the OQA. Applications to representative problems are presented with good success. © 1995 American Institute of Physics.